Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.1 - Real Numbers - 1.1 Exercises - Page 12: 92

Answer

See the steps.

Work Step by Step

\[|a-b] = \left\{ \begin{array}{lr} a-b & : a > b\\ b-a & : b>a \\ 0 &: a=b \end{array} \right. \] For $a>b$: $$\dfrac{a+b+|a-b|}{2}= \dfrac{a+b+a-b}{2}\\ = \dfrac{2a}{2} = a$$ For $b>a$: $$\dfrac{a+b+|a-b|}{2}= \dfrac{a+b+b-a}{2}\\ = \dfrac{2b}{2} = b$$ $\therefore max(a,b) = \dfrac{a+b+|a-b|}{2}$
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